Electrostatics
Charge Charge is quantized . Q = ne Law of Conservation of Charge = Charge can neither be created nor be destroyed , it can only be transferred from one body to another . Coulomb's Law When two charges , touch each other , the charge is equally shared by them . The electrostatic force inside a conductor is zero . F = k q1q2 / r2 where k = 1 / 4πε = 9 x 109 Nm2/C2 Superposition of Charges Charge Density λ = Q/l σ = Q/A ρ = Q/V Dipole Moment p = Q.2l Torque Torque = pEsinθ Electric Field Intensity E = F/Q E = k q / r2 (due to point charge) Due to Dipole : E = k psinθ / r3 Inside a Conductor : '''k = infinite ... E = 0 Note : Potential decreases in the direction of Electric Field Intensity . '''Due to Conductor of length L and at distance a : E = k q / r - 1/(L+a) Non-Conducting Sphere : The Electric Field Intnsity inside and outsid a non-conductor aries just like g varies wih depth and height . Electric Lines of Force # No two electric lines of force can intersect each other , they are always parallel . # Electric Lines of Force are close continuous curves and they start from positive and end on negative charge . # The tangent drawn at any instant to the lines of force , gives it direction at that instant . # The lines are more crowded where the field is strong and less crowded where the field is weak . # When two unlike charges are placed close to each other , the lines of force are compressed ; this explains attraction of unlike charges . # When two like charges are placed close to each other , the lines of force exert lateral pressure on each other , this explains repulsion of like charges . Electric Potential Energy U = F.r = k q1q2/r Potential Energy of System of Charges : U = U1 + U2 + U3 +.......+ Un Potential Energy of Dipole in an External Field : U = -pEcosθ Wor done in rotating a dipole from θ1 to θ2 = - pE (cosθ1 - cos θ2) Electric Potential V = U/q = F.r / q = k q/r V = Er = U/Q ... U = VQ The sign of Potential depends on like/unlike charges . Cases of Potential : # Due to point charge : V = - kq/r ... at r = 0 , Z is negative infinite . The graph will be negative , curved and parallel to V and r axes . # Inside a Solid Sphere : '''V = - kq (1.5R2 - 0.5r2) / R3 . At r=R ,V = - kq/'R . At r = 0 ,V = -1.5kq'/'R The graph is negative , parabolic . # '''Outside a Solid Sphere : '''V = -kq/r , at r = infinity , V = 0 ; On surface , V = -kq/R # '''Due to a Spherical Shell : '''Outside ' V = -kq/r . Inside V = - kq/r # '''On the Axis of a Ring : '''V = - kq / sqrt(R2+x2) '''Due to Dipole : V = k pcosθ / r2 At an equatorial point , the electric potential is zero Note : Potential decreases in the direction of Electric Field Intensity . Common Potential Suppose two spheres of radii r1 & r2 are connected by a wire and charges q1 & q2 are residing on their surfaces then Common Potential = + q2 / 4πε(r1+r2) Potential Difference VAB = VA - VB Electric Flux Φ = Edscosθ Gauss' Theorem NEI = εE TNEI = ∫ NEI = ∫ εE dscosθ The Gauss's Law '''states that the Total Normal Electric Induction is equal to the algebraic sum of the Charges enclosed by the surface . '''TNEI = Qi Applications of Gauss's Law # Sphere : E = 1 / 4πε0 q/r2 # Cylinder : E = λ/2πε0r # Any Shape : E = σ/ε0 # Sheet : E = σ/2ε0 Mechanical Force Mechanical Force per Unit Area = 1/2 E2ε = 1/2 σ2/ε Energy Density Potential Energy per unit Volume = 1/2 E2ε = 1/2 σ2/ε Dielectrics and Polarization Polar Non-Polar Electric Moments Polarization = P = σp {Amount of charge induced due to external electric field} Capacitance Q = CV C = Q/V C = Aε / d Series Combination : Cs = 1/C1 + 1/C2 + 1/C3 + .... +1/Cn Parallel Combination : Cp = C1 + C2 + C3 + .... + Cn Energy Stored in a Capacitor : E = 1/2 CV2 Force between the plates of Capacitor : F = Q2 / 2Aε C = kCo Van de Graaff Generator Tips and Tricks 1) For repulsive force between two like charges , the closest distance of approach is when Kinetic Energy is equal to Potential Energy . 2) For questions related to Flux and Electric Field Intensity , consider Gauss Theorem . The formulae for E , at diffrent distances from a conductor , circuar conductor and at centre of circular conductor is the sam as B . Category:Physics